LETTER TO PROFESSOR NERNST.
[Gonseil scientifique sous les auspices de M. Ernest Solvay, Oct. 1911.]
DEAR PROF. NERNST,
Having been honoured with an invitation to attend the Conference at Brussels, I feel that the least that I can do is to communicate my views, though I am afraid I can add hut little to what has been already said upon the subject.
I wish to emphasize the difficulty mentioned in my paper of 1900* with respect to the use of generalized coordinates. The possibility of representing the state of a body by a finite number of such (short at any rate of the whole number of molecules) depends upon the assumption that a body may be treated as rigid, or incompressible, or in some other way simplified. The justification, and in many cases the sufficient justification, is that a departure from the simplified condition would involve such large amounts of potential energy as could not occur under the operation of the forces concerned. But the law of equi-partition lays it down that every mode is to have its share of kinetic energy. If we begin by supposing an elastic body to be rather stiff, the vibrations have their full share and this share cannot be diminished by increasing the stiffness. For this purpose the simplification fails, which is as much as to say that the method of generalized coordinates cannot be applied. The argument becomes, in fact, self-contradictory.
Perhaps this failure might be invoked in support of the views of Planck and his school that the laws of dynamics (as hitherto understood) cannot be applied to the smallest parts of bodies. But I must confess that I do not like this solution of the puzzle. Of course I have nothing to say against following out the consequences of the [quantum] theory of energy—a procedure which has already in the hands of able men led to some interesting
* Phil. Mag. Vol. xux. p. 118 ; Scientific Papers, Vol. iv. p. 451.time is that mso+^^i —^ z Khali remain unchanged. Thus the amplitude which is to be found at #=0 on the screen prevails also behind the screen along the line